Well, if you don't trust Jill's years of experience working with thousands of websites, I'm not sure what additional information anyone else can offer that will convince you, but here goes...
The company I work for has more than one website (and in addition, our main website is made up of multiple domains). One domain included in the main site is our online store, which includes information on all our products. We also have three product-specific "mini sites" that give more detail about some of our products. Although each of the three detail sites contain information about products that are also included in the online store, there isn't any duplicate content between any of these sites. (While there are only three product "mini sites" today, we have in the past had as many as five product detail sites active at one time. With no issues noted.)
All our sites are are hosted on the same server. In fact, all three of these mini sites share the same IP address with one of the domains that make up our main site. The main site has been in place for over 10 years. The first of the detail product sites went up in 2004. And we have had no issues at all with Google at any time.
Edited to add: I should also note that we freely interlink among all our sites -- mini sites and main site / among the different domains that make up the main site. We're very up-front about the fact that these sites are ours and that we're not trying to hide anything from anybody.
Edited by torka, 30 January 2013 - 09:55 AM.